Knowledge that Transforms

Competition is often associated with the idea that there are many traders in the market or that each price maker is small as compared to the market. This paper introduces this notion of market size in a model of price competition with imperfect substitutes by constructing a model which creates a bridge between the Chamberlin and Bertrand-Edge worth lines of work on price competition. We investigate the role of two fundamental parameters in the existence of an equilibrium: the market size, given by the number n of competitors, and the degree of substitutability. We prove that: (a) For a given number of n ≦ 2 of competitors, a sufficiently large but finite degree of substitutability entails nonexistence. This thus generalizes the Bertrand-Edgeworth nonexistence result, which applies only to perfect substitutes, (b) Conversely for a given upper bound on the degree of substitutability, a sufficiently large number of competitors ensures existence, which thus introduces a significant role for market size in models of imperfect competition. We finally investigate the proximity of an equilibrium (when it exists) to a “competitive outcome”, and we find that both high substitutability and large market size are a condition for competitiveness.

We study a union formation decision problem when workers consist of two groups distinguished by different productivities. Workers may form either a joint union or two separate unions. The whole decision process is modelled as an extensive-form bargaining game. Workers form a joint union when the sizes or productivities of the groups are similar. In the first case, there is a wage differential which is more (less) than proportional to the productivity difference if the size of the more productive is smaller (larger) than that of the less productive. In the second case, there is no wage differential.

This paper considers the problem of designing mechanisms whose Nash allocations coincide with the Lindahl allocations for public goods economies with more than one private good. Unlike previous mechanisms, the mechanism presented here has a single-valued, feasible, and continuous outcome function. Furthermore, when there are no public goods in economies, feasible and continuous implementation of the (constrained) Walrasian correspondence can be obtained as a corollary of our Theorem 1.

The paper analyzes an infinite-horizon sequential bargaining game (with one-sided offers) between a buyer and a seller when the buyer's valuation depends on the seller's; the seller knows the value of the object and the buyer does not. The influence of relative discount factors on the solution is studied. It is shown, for example, that an impasse may result if the buyer (offeror) is too impatient relative to the seller: the buyer makes a single take-it-or-leave-it offer.

Standard economic intuition would say that private provision of public goods will be inefficient due to free-rider problems. This view is in contrast to the results in the literature on full implementation where it is shown that (under certain conditions) games exist which only have efficient equilibria. The games usually used to demonstrate existence are quite complex and seem “unnatural” possibly leading to the perception that implementation requires a central authority to choose and impose the game. In a simple public goods setting, we show that a very natural game—similar to one often used elsewhere in the literature to model private provision—in fact fully implements the core of this economy in undominated perfect equilibria. More specifically, we consider a complete information economy with one private good and two possible social decisions. Agents voluntarily contribute any non-negative amount of the private good they choose and the social decision is to provide the public good iff contributions are sufficient to pay for it. The contributions are refunded otherwise. The set of undominated perfect equilibrium outcomes of this game is exactly the core of the economy. We give some extensions of this result, discuss the role of perfection and alternative equilibrium notions, and discuss the intuition and implications of the results.